Conformally-projectively flat statistical structures on tangent bundles over statistical manifolds

The non-parametric version of Information Geometry has been developed in recent years. The first basic result was the construction of the manifold structure on ℳμ, the maximal statistical models associated to an arbitrary measure μ (see Ref. 48). Using this construction we first show in this paper that the pretangent and the tangent bundles on ℳμ are the natural domains for the mixture connection and for its dual, the exponential connection. Second we show how to define a generalized Amari embedding AΦ:ℳμ→SΦ from the Exponential Statistical Manifold (ESM) ℳμ to the unit sphere SΦ of an arbitrary Orlicz space LΦ. Finally we show that, in the non-parametric case, the α-connections ∇α(α∈(-1,1)) must be defined on a suitable α-bundle ℱα over ℳμ and that the bundle-connection pair (ℱα, ∇α) is simply (isomorphic to) the pull-back of the Amari embedding Aα: ℳμ→S2/1-α were the unit sphere S2/1-αcL2/1-α is equipped with the natural connection.

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Conformally-projectively flat trans-Sasakian statistical manifolds

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2019.122441 ◽

2019 ◽

Vol 535 ◽

pp. 122441

Author(s):

Ahmet Kazan

Keyword(s):

Projectively Flat ◽

Statistical Manifolds

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ON A PERFECT FLUID KÂ¨ AHLER SPACETIME

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v12i3.44 ◽

2016 ◽

Vol 12 (3) ◽

pp. 4350-4355

Author(s):

VIBHA SRIVASTAVA ◽

P. N. PANDEY

Keyword(s):

Field Equation ◽

Perfect Fluid ◽

Sectional Curvature ◽

Einstein Field Equation ◽

Cosmological Term ◽

Conformal Killing ◽

Killing Vectors ◽

Projectively Flat ◽

Conformal Killing Vectors

The object of the present paper is to study a perfect fluid KÂ¨ahlerspacetime. A perfect fluid KÂ¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid KÂ¨ahler spacetime have been obtained. Dust model for perfect fluid KÂ¨ahler spacetime has also been studied.

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New cases of integrable systems with dissipation on the tangent bundles of multi-dimensional manifolds

Доклады Академии наук ◽

10.31857/s086956520003039-5 ◽

2018 ◽

Vol 482 (5) ◽

pp. 527-533

Author(s):

M. Shamolin ◽

Keyword(s):

Integrable Systems ◽

Tangent Bundles

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Chern-Simons invariants and heterotic superpotentials

Journal of High Energy Physics ◽

10.1007/jhep09(2020)141 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Lara B. Anderson ◽

James Gray ◽

Andre Lukas ◽

Juntao Wang

Keyword(s):

Heterotic String ◽

New Techniques ◽

Vacuum Stability ◽

Large Classes ◽

Moduli Stabilization ◽

String Compactifications ◽

Key Features ◽

Effective Theories ◽

Chern Simons ◽

Tangent Bundles

Abstract The superpotential in four-dimensional heterotic effective theories contains terms arising from holomorphic Chern-Simons invariants associated to the gauge and tangent bundles of the compactification geometry. These effects are crucial for a number of key features of the theory, including vacuum stability and moduli stabilization. Despite their importance, few tools exist in the literature to compute such effects in a given heterotic vacuum. In this work we present new techniques to explicitly determine holomorphic Chern-Simons invariants in heterotic string compactifications. The key technical ingredient in our computations are real bundle morphisms between the gauge and tangent bundles. We find that there are large classes of examples, beyond the standard embedding, where the Chern-Simons superpotential vanishes. We also provide explicit examples for non-flat bundles where it is non-vanishing and non-integer quantized, generalizing previous results for Wilson lines.

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